Alemdar Hasanov

Alemdar Hasanov
Kocaeli University · Department of Advertising

PhD, Doctor of Science

About

66
Publications
2,331
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517
Citations

Publications

Publications (66)
Article
In this paper, we study the inverse problem of determining an unknown spatial load $F(x)$ in the damped non-homogeneous isotropic rectangular Kirchhoff-Love plate equation $\rho_h(x) u_{tt}+\mu (x) u_{t}+\left (D(x)(u_{x_1x_1}+\nu u_{x_2x_2})\right )_{x_1x_1} + \left (D(x)(u_{x_2x_2}+\nu u_{x_1x_1})\right )_{x_2x_2} + 2(1-\nu)\left (D(x)u_{x_1x_2}\...
Chapter
In this chapter we consider some inverse problems for the Maxwell equations. Here H = (H1, H2, H3) and E = (E1, E2, E3) are vectors of electric and magnetic strengths, ε > 0, μ > 0 and σ are the permittivity, permeability and conductivity coefficients, respectively, which define electro-dynamical parameters of a medium. The function j = j(x, t) is...
Chapter
The problem of recovering the sound speed (or index of refraction) from travel time measurements is an important issue in determining the substructure of the Earth. The same inverse problem can also be defined as the problem of reconstructing of a Riemannian metric inside a compact domain Ω from given distances of geodesics joining arbitrary couple...
Chapter
Beams and plates are important parts of main engineering constructions such as aircraft wings, flexible robotic manipulators, large space structures and robots, marine risers and moving strips. Within the scope of the linear theory of elasticity, classical Euler-Bernoulli beam and Kirchhoff plate theories have been a cornerstone tools in engineerin...
Chapter
In the first part of this chapter we study two inverse source problems related to the second order hyperbolic equations utt − uxx = ρ(x, t)g(t) and utt − uxx = ρ(x, t)φ(x) for the quarter plane \(\mathbb {R}^2_+=\{(x,t)|\, x>0, t>0\}\), with Dirichlet type measured output f(t) := u(x, t)|x=0. The time-dependent source g(t) and the spacewise-depende...
Chapter
Inverse source problems for evolution PDEs ut = Au + F, t ∈ (0, T], represent a well-known area in inverse problems theory and have extensive applications in various fields of science and technology. These problems play a key role in providing estimations of unknown and inaccessible source terms involved in the associated mathematical model, using...
Chapter
The main objective of this chapter is to present some necessary results of functional analysis, frequently used in study of inverse problems. For simplicity, we derive these results in Hilbert spaces. Let H be a vector space over the field of real (\(\mathbb {R}\)) or complex (\(\mathbb {C}\)) numbers.
Chapter
This Chapter deals with inverse coefficient problems for linear second-order 1D parabolic equations. We establish, first, a relationship between solutions of direct problems for parabolic and hyperbolic equations. Then using the results of Chap. 3 we derive solutions of the inverse problems for parabolic equations through the corresponding solution...
Chapter
Inverse problems for wave equations have been extensively studied in the last 50 years due to a large number of engineering and technological applications. The objective of this chapter is to present an analysis of the two basic inverse coefficient problems related to 1D damped wave equations m(x)utt + μ(x)ut = (r(x)ux)x and \(m(x) u_{tt}+\mu (x)u_...
Chapter
Inverse problems arise in almost all areas of science and technology, in modeling of problems motivated by various physical and social processes. Most of these models are governed by differential and integral equations. If all the necessary inputs in these models are known, then the solution can be computed and behavior of the physical system under...
Chapter
Inverse problems related to the transport equations arise in many areas of applied sciences and have various applications in medical imaging and tomography. At least the three techniques—X ray tomography, single particle emission tomography and positron emission tomography—are based on the transport equations. On the other hand, mathematical models...
Chapter
This chapter is an introduction to the basic inverse problems for elliptic equations. One class of these inverse problems arises when the Born approximation is used for scattering problem in quantum mechanics, acoustics or electrodynamics. In the first part of this chapter two inverse problems, the inverse scattering problem at a fixed energy and t...
Book
This book presents a systematic exposition of the main ideas and methods in treating inverse problems for PDEs arising in basic mathematical models, though it makes no claim to being exhaustive. Mathematical models of most physical phenomena are governed by initial and boundary value problems for PDEs, and inverse problems governed by these equatio...
Article
In this study, solvability of the initial boundary value problem for general form Euler–Bernoulli beam equation which includes also moving point-loads is investigated. The complete proof of an existence and uniqueness properties of the weak solution of the considered equation with Dirichlet type boundary conditions is derived. The method used here...
Article
This work is a further development of weak solution theory for the general Euler–Bernoulli beam equation ρ(x)utt+μ(x)ut+r(x)uxxxx−(Tr(x)ux)x=F(x,t) defined in the finite dimension domain ΩT≔(0,l)×(0,T)⊂R², based on the energy method. Here r(x)=EI(x), E>0 is the elasticity modulus and I(x)>0 is the moment of inertia of the cross-section, ρ(x)>0 is t...
Article
Full-text available
This paper studies the Lipschitz continuity of the Fréchet gradient of the Tikhonov functional {J(k):=(1/2)\lVert u(0,\cdot\,;k)-f\rVert^{2}_{L^{2}(0,T)}} corresponding to an inverse coefficient problem for the {1D} parabolic equation {u_{t}=(k(x)u_{x})_{x}} with the Neumann boundary conditions {-k(0)u_{x}(0,t)=g(t)} and {u_{x}(l,t)=0} . In additio...
Book
This book presents a systematic exposition of the main ideas and methods in treating inverse problems for PDEs arising in basic mathematical models, though it makes no claim to being exhaustive. Mathematical models of most physical phenomena are governed by initial and boundary value problems for PDEs, and inverse problems governed by these equatio...
Chapter
Here \(H=(H_1,H_2,H_3)\) and \(E=( E_1,E_2,E_3)\) are vectors of electric and magnetic strengths, \(\varepsilon >0\), \(\mu >0\) and \(\sigma \) are the permittivity, permeability and conductivity coefficients, respectively, which define electro-dynamical parameters of a medium.
Chapter
Inverse problems related to the transport equations arise in many areas of applied sciences and have various applications in medical imaging and tomography.
Chapter
This Chapter deals with inverse coefficient problems for linear second-order 1D parabolic equations. We establish, first, a relationship between solutions of direct problems for parabolic and hyperbolic equations.
Chapter
Inverse source problems for evolution PDEs \(u_t=Au+F\), \(t\in (0,T_f]\), represent a well-known area in inverse problems theory and has many engineering applications.
Chapter
The problem of recovering the sound speed (or index of refraction) from travel time measurements is an important issue in determining the substructure of the Earth.
Chapter
In the first part of this chapter we study two inverse source problems related to the second order hyperbolic equations \(u_{tt}-u_{xx}=\rho (x, t)g(t)\) and \(u_{tt}-u_{xx}=\rho (x, t)\varphi (x)\) for the quarter plane \(\mathbb {R}^2_+=\{(x, t)|\, x>0, t>0\}\), with Dirichlet type measured output data \(f(t):=u(x, t)\vert _{x=0}\).
Chapter
The main objective of this chapter is to present some necessary results of functional analysis, frequently used in study of inverse problems.
Chapter
Inverse problems arise in almost all areas of science and technology, in modeling of problems motivated by various physical and social processes.
Chapter
This chapter is an introduction to the basic inverse problems for elliptic equations.
Article
In this paper, we consider an inverse coefficient problem for the linearized Korteweg–de Vries (KdV) equation ut+ux⁢x⁢x+(c⁢(x)⁢u)x=0, with homogeneous boundary conditions u⁢(0,t)=u⁢(1,t)=ux⁢(1,t)=0, when the Neumann data g⁢(t):=ux⁢(0,t), t∈(0,T), is given as an available measured output at the boundary x=0. The inverse problem is formulated as a mi...
Article
Two types of inverse source problems of identifying asynchronously distributed spatial loads governed by the Euler–Bernoulli beam equation , with hinged–clamped ends (), are studied. Here are linearly independent functions, describing an asynchronous temporal loading, and are the spatial load distributions. In the first identification problem the v...
Article
In this article, we study an inverse problem of reconstructing a space dependent coefficient in a generalized Korteweg–de Vries (KdV) equation arising in physical systems with variable topography from final time overdetermination data. First the identification problem is transformed into an optimization problem by using optimal control framework an...
Article
In this study, we investigate the inverse problem of identifying an unknown spacewise-dependent source F(x) in the one-dimensional advection-diffusion equation ut=Duxx - vux + F (x)H(t), (x, t) ∈ (0, 1)×(0, T], based on boundary concentration measurements g(t):= u (ℓ, t). Most studies have attempted to reconstruct an unknown spacewise-dependent sou...
Chapter
Full-text available
We study coefficient inverse problems arising in modeling of resistivity prospecting problems. Numerical simulations are investigated in the cases of vertically and cylindrically layered medium. Conductivity coefficients are assumed to be sufficiently smooth 1D functions. The model leads to an inverse problem of identification of an unknown coeffic...
Article
Full-text available
An adjoint problem approach with subsequent conjugate gradient algorithm (CGA) for a class of problems of identification of an unknown spacewise dependent source in a variable coefficient parabolic equation ut=(k(x)ux)x+F(x)H(t)ut=(k(x)ux)x+F(x)H(t), (x,t)∈(0,l)×(0,T](x,t)∈(0,l)×(0,T] is proposed. The cases of final time and time-average, i.e. inte...
Article
The problem of determining an unknown source term in a linear parabolic equation ut=(k(x)ux)x+F(x,t), (x,t)∈ΩT, from the Dirichlet type measured output data h(t):=u(0,t) is studied. A formula for the Fréchet gradient of the cost functional J(F)=‖u(0,t;F)−h(t)‖2 is derived via the solution of the corresponding adjoint problem, within the weak soluti...
Article
This article presents a computational analysis of the adjoint problem approach for parabolic inverse coefficient problems based on boundary measured data. The proposed coarse-fine grid algorithm constructed on the basis of this approach is an effective computational tool for the numerical solution of inverse coefficient problems with various Neuman...
Article
This article presents a computational analysis of the Conjugate Gradient Method (CGM), and a comparative analysis of the method (CGM) and coarse-fine grid algorithm (CFGA) for parabolic inverse coefficient problems (ICPs) based on boundary measured data. The adjoint problem approach is applied to obtain formal gradients of each ICPs as the L 2-scal...
Article
Full-text available
This article presents a mathematical and computational analysis of the adjoint problem approach for parabolic inverse coefficient (or inverse heat conduction) problems based on boundary measured data. In Part I the mathematical analysis is given for three classes of typical inverse coefficient problems with various Neumann or/and Dirichlet types of...
Article
A new method of determining elastoplastic properties of a beam from an experimentally given value T, T (φ) of torque (or torsional rigidity), during the quasistatic process of torsion, given by the angle of twist φ ∈ [φ*, φ *], is proposed. The mathematical model leads to the inverse problem of determining the unknown coefficient g = g (ξ2), ξ = |...
Article
Full-text available
The nonlocal identification problem related to nonlinear ion transport model including diffusion and migration is studied. Ion transport is assumed to be superposition of diffusion and migration under the influence of an electric field. Mathematical modeling of the experiment leads to an identification problem for a strongly nonlinear parabolic equ...
Article
Full-text available
An inverse problem related to the determination of elastoplastic properties of a beam is considered within J 2 deformation theory. A new fast algorithm is proposed for the identification of elastoplastic properties of engineering materials. This algorithm is based on finding the three main parameters of the unknown curve g(ξ²) (plasticity function)...
Article
This article presents numerical implementation of the approach proposed in the previous study (Identification of the unknown diffusion coefficient in ion transport problem. I. The theory, Math. Chem. (2009) (submitted)) for the coefficient inverse problems related to linear diffusion equation in chronoamperometry. The coarse-fine grid algorithm is...
Article
The nonlocal identification problem related to nonlinear ion transport model including diffusion and migration is studied. Ion transport is assumed to be superposition of diffusion and migration under the influence of an electric field. Mathematical modeling of the experiment leads to an identification problem for a strongly nonlinear parabolic equ...
Article
Inverse problems of determining the unknown source term F(x, t) in the cantilevered beam equation utt = (EI(x)uxx)xx + F(x, t) from the measured data μ(x) := u(x, T) or ν(x) := ut(x, T) at the final time t = T are considered. In view of weak solution approach, explicit formulae for the Fréchet gradients of the cost functionals J1(F) = ||u(x, T; w)...
Article
Linear and nonlinear boundary value problems related to elastic and elastoplastic torsional rigidity of a beam are considered. As a sample model, pure elastic torsion problem for a square cross section bar is solved by the method of separation variables. The well-known analytical formula tot torsional rigidity is obtained, The nonlinear boundary va...
Article
Ion transport problem related to controlled potential experiments in electrochemistry is studied. The problem is assumed to be superposition of diffusion and migration under the influence of an electric field. The comparative analysis are presented for three well-known models—pure diffusive (Cottrell’s), linear diffusion-migration, and nonlinear di...
Article
Mathematical models of ion transport in a potential field are analyzed. Ion transport is regarded as the superposition of diffusion and migration. The explicit analytical formulaes are obtained for the concentration of the reduced species and the current response in the case of pure diffusive as well as diffusion–migration model, for various initia...
Article
This study is related to inverse coefficient problems for a nonlinear parabolic variational inequality with an unknown leading coefficient in the equation for the gradient of the solution. An inverse method, involving minimization of a least-squares cost functional, is developed to identify the unknown coefficient. It is proved that the solution of...
Article
The mathematical models of the ion transport problem in a potential field are anayzed. Ion transport is regarded as the superposition of diffusion and convection. In the case of pure diffusion model the classical Gottrell’s result is studied for a constant as well as for the time dependent Dirichlet data at the electrode. Comparative analysis of th...
Article
Full-text available
This article presents a mathematical and numerical analysis of the adjoint problem approach for inverse coefficient problems related to linear parabolic equations. Based on maximum principle a structure of the coefficient-to-data mapping is derived. The obtained integral identities permit one to prove the monotonicity and invertibility of the input...
Article
We study the problems of solvability and linearization for the nonlinear boundary value problems with nonlinear operator Au := -(k ((u')(2)) u')' + g (u). Solvability in H-1[a,b] of the problems is obtained by using monotone potential operator theory and Browder-Minty theorem. Sufficient conditions for the solvability are obtained in explicit form....
Article
This paper deals with the problem of determining the leading coefficient k ¼ kððu 0 Þ 2 Þ of the nonlinear (monotone potential) Sturm-Liouville operator Au ¼� ð kððu 0 Þ 2 Þu 0 ðxÞÞ 0 þ qðxÞuðxÞ, x 2ð a; bÞ. As an additional condition only two measured data at the boundary (x ¼ a, x ¼ b) are used. Solvability and linearization of the corresponding...
Article
We study the problem of determining the leading coecient k ˆ k…x† of the Sturm± Liouville operator Au À…k…x†u H …x†† H ‡ q…x†u…x†; x P …a; b†, from a measured data given in the form of Dirichlet or/and Neumann type (additional) boundary conditions. The contribution of the each measured data to the unicity of the inverse problem solution is analyse...
Article
Computational method for the Signorini problem in 2D is presented. Using qualitative properties of the solution on a perturbed boundary the iteration method for finding of the unknown boundary Γc is constructed. In the first part of the method the boundary ac=∂Γc is localized within two mesh points of a fixed FE mesh. In the second part introducing...
Article
Qualitative properties of solutions of the unilateral elliptic problem and of the Signorini problem for the Lame system of equations are considered. A preliminary analysis reduces each of the nonlinear problems to a mixed linear problem and to additional conditions (in the form of inequalities) on the part of the boundary. In each case, it is shown...
Article
In this paper the class of inverse coefficient problems for nonlinear monotone potential elliptic operators is considered. This class is characterized by the property that the coefficient of elliptic operator depends on the gradient of the solution, i.e. on . The unknown coefficient is required to belong to a set of admissible coefficients which is...
Article
The class of inverse problems for a nonlinear elliptic variational inequality is considered. The nonlinear elliptic operator is assumed to be a monotone potential. The unknown coefficient of the operator depends on the gradient of the solution and belongs to a set of admissible coefficients which is compact in . It is shown that the nonlinear opera...
Article
In this paper, we propose a mathematical model of a problem related to the determination of elasto-plastic properties of a deformable axisymmetric isotropic material using an experimentally given penetration diagram. The considered physical model is based on elasto-plastic deformation theory. The problem leads to an inverse coefficient problem for...
Article
The method of definition of elastoplastic properties of constructive materials on the basis of the diagram of inculculation in the process of loading of material is suggest.

Projects

Project (1)
Project
The purpose of the research is to construct mathematical and computational framework of the class of inverse coefficient and source problems for the general form Euler-Bernoulli equation from all three following types of available boundary measured data: measured deflection, slope and moment.